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Newton’s Law of Gravitational Force Formula
The Law of Gravitation gives the Gravitational Force (F) between two bodies of masses (m1 and m2) at a distance r (as shown in Figure) , apart from their centers, is given as:
F ∝ m1m2
F ∝ 1/r2
Now, combining the above two relations as,
F ∝ m1m2 / r2
F = Gm1m2 / r2
where G is the proportionality constant known as Gravitational Constant (= In SI Unit 6.67 ×10−11N⋅ m2/kg2 or in CGS Unit In CGS units: 6.67×10-8 dyne cm2 g-2).
Unit of Gravitational Force
- SI unit of Gravitational Force is Newton (N).
- Dimensional Formula of Gravitational Force is [M1L1T-2].
Properties of Gravitational Force
Here are some important characteristic features of Gravitational Force,
- Gravitational forces are always attractive and the weakest of all the fundamental forces.
- It is a type of Non-Contact Force, as it does not require any physical contact or touch to be experienced by a system of objects.
- Gravitational Force is a Long-range force and does not require any medium.
- The Gravitational Force value at the surface of the Earth is constant.
Newton’s Law of Gravitation – Important Concepts & FAQs
Q1: What is Newton’s Law of Gravitation?
A: Newton’s Law of Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it is expressed as: expressed as:
F = Gm1m2 / r2
Where:
- F = Gravitational force
- G = Universal gravitational constant
- m1 and m2 = Masses of two objects
- r = Distance between their centers
Q2: Who discovered the Law of Gravitation and how?
A: Sir Isaac Newton formulated the Law of Gravitation in 1665 when he observed an apple falling from a tree. He realized that the same force that pulls the apple towards the ground also governs the motion of the Moon around the Earth.
Q3: What is the significance of Newton’s Law of Gravitation?
A: The law explains:
- Why objects fall towards Earth.
- The motion of planets around the Sun.
- The force acting between celestial bodies.
- The concept of weight and free-fall acceleration.
MCQs on Newton’s Law of Gravitation
Q1: What happens to the gravitational force if the distance between two objects is doubled?
- (A) It becomes half
- (B) It becomes one-fourth
- (C) It doubles
- (D) It remains the same
Correct Answer: (B) It becomes one-fourth
Explanation: According to Newton’s Law, force is inversely proportional to the square of the distance F ∝ 1/r2. When r is doubled, F decreases by a factor of 22=4.
Q2: Which of the following statements is true about gravitational force?
- (A) It acts only on Earth.
- (B) It acts between any two objects in the universe.
- (C) It is independent of mass.
- (D) It does not affect celestial bodies.
Correct Answer: (B) It acts between any two objects in the universe.
Explanation: Newton’s Law states that all objects with mass experience gravitational attraction, regardless of their location in the universe.
Q3: If the mass of an object is doubled, how does the gravitational force change?
- (A) It becomes half
- (B) It remains the same
- (C) It doubles
- (D) It becomes four times
Correct Answer: (C) It doubles
Explanation: The gravitational force FF is directly proportional to the product of masses F ∝ m1m2. If one of mass doubles, the force also doubles.
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